Intern
ati
o
n
a
l Jo
urn
a
l
o
f
R
o
botics
a
nd Au
tom
a
tion
(I
JR
A)
Vol
.
2
,
No
. 2,
J
une
2
0
1
3
,
pp
. 56~
6
8
I
S
SN
: 208
9-4
8
5
6
56
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJRA
Modeling and Control of 5DOF
Robot
Arm Using Fuzzy L
ogi
c
Supervisory Control
Mohammad Amin Rashidi
f
ar
1
, Ali
Amin Ra
shidifa
r
2
,
Dar
v
ish Ah
m
a
di
1
1
Departm
e
nt of M
echani
cal
Eng
i
neering
,
Is
l
a
m
i
c A
zad Unive
r
s
i
t
y
, S
h
adeg
an Br
an
ch, S
h
ad
egan
, Ir
an
2
Departm
e
nt
of
Com
puter S
c
ien
ce,
Is
lam
i
c
Azad
Univers
i
t
y
,
S
h
a
d
egan Br
anch
, S
h
adegan
, Ir
an
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 22, 2013
Rev
i
sed
Ap
r
20
, 20
13
Accepte
d
May 6, 2013
Modeling and
control of 5 d
e
gree of fre
edom (DOF) robot arm is the subject
of this article.
The modeling problem
is necessar
y
befor
e
apply
i
ng con
t
ro
l
techn
i
ques
to gu
arant
ee th
e ex
ec
ution of an
y t
a
s
k
accord
ing to a d
e
s
i
red inpu
t
with minimum
error. Der
i
ving
both forw
ard an
d inverse kin
e
matics is an
important step
in robot modelin
g ba
sed on th
e Denavit Harten
berg (DH)
repres
ent
a
tion
.
Proportional in
tegral d
e
rivativ
e (PID) controller
is used
as
a
referen
c
e
ben
c
h
m
ark to
com
p
are i
t
s
res
u
lts
with
fuzz
y
log
i
c
cont
roller
(FLC)
and
fuzzy
super
v
isor
y
contro
ller
(FSC)
re
sults. FLC is applied as a second
controller
becau
se of the nonlin
earity
in
th
e robot manipulators.
We compare
the resul
t
of
the
PID
controller
and FLC results
in terms of time response
s
p
ecifi
cat
ions
. F
S
C
is
a h
y
br
id
between
the pr
evious two contr
o
llers.
The
FSC is used for tuning PID gains
since
PID alone
performs not satisfactor
y
in
nonline
a
r s
y
stem
s. Hence,
com
p
a
r
ison of tuning of PID param
e
ter
s
is utiliz
ed
using classical
method a
nd FS
C method. Based on si
mulation
results, FLC
gives better
res
u
lts than
classical PID
con
t
roller in terms of time response
and FSC is better than classical methods
such
as Ziegler-Nich
o
ls (ZN) in
tuning PID par
a
meters in
terms of
time response.
Keyword:
Fuzzy logic c
o
ntroller
Kin
e
m
a
tic an
alysis
Li
nearc
ont
rol
Non
lin
earcon
tro
l
Copyright ©
201
3 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Mo
h
a
mm
ad
Amin
Rash
id
ifar
Depa
rtem
ent of Mec
h
anical
Engineeri
n
g,
Islamic Azad
Uni
v
ers
ity, Shadega
n
B
r
anc
h
.
Em
a
il:
r
a
sh
id
ifar
_58
@yahoo
.co
m
1.
INTRODUCTION
In
recent years
,
industrial a
n
d co
mm
ercia
l
syste
m
s with high e
ffici
e
n
cy and
great pe
rformance ha
ve
t
a
ken a
d
vant
a
g
es of
r
o
b
o
t
t
echn
o
l
o
gy
. La
r
g
e
num
ber
of
c
o
n
t
rol
resea
r
c
h
es and n
u
m
e
rous cont
rol
a
ppl
i
c
a
t
i
ons
were
prese
n
t
e
d
du
ri
n
g
t
h
e l
a
s
t
y
ears, conce
n
t
r
at
ed o
n
co
nt
r
o
l
of
ro
b
o
t
i
c
sy
st
em
s. R
obot
m
a
ni
pul
at
o
r
fi
el
d i
s
o
n
e
of th
e i
n
terested
field
s
in
ind
u
s
t
r
ial, ed
u
cation
a
l an
d
m
e
d
i
cal ap
p
l
i
catio
n
s
.
It work
s in
un
pred
ictab
l
e,
hazard a
nd i
n
hospita
ble circum
s
t
ances whic
h hum
a
n canno
t reac
h [1-2]. For exam
pl
e, worki
n
g in c
h
e
m
ical
or
nucl
e
a
r
reac
t
o
rs i
s
ve
ry
da
nge
r
ous
, w
h
i
l
e
whe
n
a r
o
b
o
t
i
n
st
ead h
u
m
a
n i
t
i
nvol
ves
no
ri
sk t
o
hum
an l
i
f
e.
There
f
ore, m
odel
i
ng a
n
d an
al
y
s
i
s
of t
h
e
ro
b
o
t
m
a
ni
pul
at
ors a
nd a
p
p
l
y
i
ng co
nt
r
o
l
t
echni
q
u
es a
r
e
very
im
portant be
fore using them
in these circum
s
t
ances to wo
rk with
high accuracy. T
h
is
article is
me
ant to be
su
itab
l
e fo
r t
h
ese app
licatio
n
s
. On
th
e
o
t
h
e
r
sid
e
, so
m
e
u
n
i
v
e
rsities and
co
lleg
e
s
o
f
fers,
so
m
e
co
u
r
ses related
to
rob
o
tics. Th
ese cou
r
ses main
ly fo
cu
s o
n
th
e th
eo
retical co
n
cep
ts
with
ou
t g
i
v
i
n
g
m
u
ch
atten
t
i
o
n
for
co
n
t
ro
lling
d
i
fferen
t rob
o
t
man
i
pu
lato
rs in
th
e
p
r
actical
si
d
e
.
Th
is article m
a
y b
e
con
s
id
ered
as a
v
a
l
u
ab
le
ed
u
cation
a
l too
l
in
th
eir lab
o
rato
ries. Th
e essen
tial
p
r
ob
lem is
to
stu
d
y
t
h
e r
obo
t
m
a
n
i
p
u
l
ator
pr
ob
lem f
r
o
m
two
sid
e
s: th
e first on
e is th
e
math
e
m
atica
l
m
o
d
e
lin
g
of the
m
a
n
i
p
u
l
ator
an
d
t
h
e actu
a
tors,
wh
ich
in
clud
es an
anal
y
s
i
s
fo
r t
h
e
fo
r
w
ar
d
ki
ne
m
a
t
i
c
, t
h
e i
nve
rse
ki
nem
a
t
i
c
and
m
odel
i
ng t
h
e di
rect
c
u
r
r
ent
(DC
)
m
o
t
o
r
be
cause
it is an
i
m
p
o
r
tan
t
issu
e in
a
ro
bo
t m
a
n
i
p
u
l
ato
r
. Th
e second p
r
o
b
l
em
is th
e co
n
t
r
o
l
o
f
the r
o
b
o
t
m
a
n
i
pu
lato
r.
The m
a
i
n
obj
ect
i
v
e of t
h
i
s
art
i
c
l
e
i
s
concerne
d wi
t
h
de
si
gni
ng a co
nt
rol
l
e
r f
o
r t
h
e m
o
ti
on o
f
t
h
e
ro
bot
manipulator to
meet the require
m
ent
o
f
th
e
desired
t
r
aj
ect
o
r
y in
pu
t with
s
u
itable error and disturba
nce
va
lues.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Mo
del
i
n
g
a
n
d
C
ont
r
o
l
of
5
D
OF R
o
bot
Arm
Usi
n
g
Fu
zzy L
ogi
c
S
upe
rvi
s
o
r
y…
(Mo
ham
ma
d Am
in
Ra
sh
i
d
ifa
r)
57
The m
o
t
i
v
at
i
on o
f
c
ont
r
o
l
t
echni
que
desi
g
n
s t
h
e
usa
g
e o
f
t
h
e
hi
g
h
p
r
e
c
i
s
i
on
per
f
o
r
m
a
nce o
f
t
h
e
ro
b
o
t
m
a
ni
pul
a
t
ors i
n
c
o
m
p
l
i
c
at
ed an
d haza
r
d
o
u
s e
nvi
ro
nm
ent
s
. Va
ri
o
u
s c
ont
rol
l
e
rs
ha
ve
been
desi
g
n
e
d
and
appl
i
e
d i
n
t
h
e ro
b
o
t
m
a
ni
pul
at
or. T
h
e fi
rst
que
st
i
on t
h
at
m
a
y
ari
s
e i
s
t
h
e di
ffe
rent
t
y
p
e
s of t
h
ese c
o
nt
r
o
l
l
e
rs
an
d th
e
d
i
fferen
ce
b
e
tween
th
ese con
t
ro
llers in
term
s
o
f
b
e
st p
e
rforman
ce will
b
e
sh
own
.
Pro
portio
n
a
l
Inte
gral De
riva
tive (PI
D
) co
nt
roller m
a
y
be the m
o
st wide
ly u
s
ed
con
t
ro
ll
er in
th
e i
n
du
st
rial an
d
co
mmercial
ap
p
lication
s
for th
e early d
e
cad
e
s,
d
u
e
to
its si
m
p
lici
t
y o
f
d
e
sign
ing
and
i
m
p
l
e
m
en
tatio
n
,
so
th
e first atte
m
p
t
i
s
t
o
appl
y
PID co
nt
rol
;
h
o
w
eve
r
, P
I
D d
o
e
s not
gi
ve
o
p
ti
m
a
l p
e
rform
a
n
ce du
e to
the
nonlinear elements.
Robot m
a
nipulators are classi
fied as non
lin
ear syste
m
s, so
classical co
n
t
ro
llers are no
t su
fficien
t
to
g
i
ve th
e
best re
sults.
F
u
zzy
lo
gic c
o
n
t
roller
(FLC
)
was
fo
u
n
d
to
be a
n
e
ffi
ci
ent
t
ool
t
o
c
o
nt
r
o
l
no
nl
i
n
ea
r sy
s
t
em
s.
Designing and testing FLC will be shown as a second
option. In
recent years,
hybrid between fuzz
y and
cl
assi
cal
cont
r
o
l
l
e
rs
has c
o
m
b
i
n
e
d
t
o
desi
g
n
a c
ont
rol
l
e
r s
u
ch
as f
u
zzy
p
l
us PI
D a
n
d f
u
zzy
l
ogi
c s
upe
rvi
s
ory
(FLS
) creat
es
m
o
re appr
op
ri
at
e sol
u
t
i
on t
o
cont
rol
r
o
b
o
t
m
a
ni
pul
at
o
r
. T
h
r
o
ug
h t
h
e art
i
c
l
e
, FLC
i
s
consi
d
e
r
ed
as an i
m
port
a
n
t
cont
r
o
l
l
e
r f
o
r
on
-l
i
n
e t
u
ni
n
g
of P
I
D
pa
ram
e
t
e
rs. FLC
m
a
y
desi
gn t
o
m
oni
t
o
r a
n
d en
ha
nce t
h
e
PID
par
a
m
e
t
e
r
s
onl
i
n
e
.
The
r
o
b
o
t
m
ovem
e
n
t
s'
anal
y
s
i
s
i
s
im
port
a
nt
bef
o
r
e
t
h
e im
pl
em
ent
a
t
i
on
of t
h
e
act
ual
syste
m
in orde
r to pre
v
ent
possible environmental hazards
.
The
r
efore
,
com
puter
sim
u
l
a
ti
ons a
r
e i
m
port
a
nt
t
o
per
f
o
r
m
any
cont
rol
l
e
r,
w
h
e
r
e de
vel
o
pi
n
g
di
st
i
n
ct
m
a
t
h
em
at
i
cal
m
odel
for a
n
y
ro
b
o
t
m
a
ni
pul
at
or
i
s
an
i
m
p
o
r
tan
t
issu
e to
p
e
rform
th
e
si
m
u
l
a
ti
ons
.
2. LI
NEA
R
A
N
D
N
O
NLI
N
EAR
CO
NT
R
O
L
There
are t
w
o
m
e
t
hods
use
d
i
n
co
nt
r
o
l
t
h
eory
t
o
c
o
nt
r
o
l
sy
st
em
s, l
i
n
ear m
e
t
hod an
d
no
nl
i
n
ea
r
m
e
t
hod.
Usi
n
g
l
i
n
ear cont
rol
i
s
appl
i
cabl
e
o
n
l
y
whe
n
t
h
e cont
rol
l
e
d sy
st
e
m
can be
m
o
d
e
l
e
d
m
a
t
h
em
ati
cal
ly
[3].
The
facts
that the m
a
jori
ty of
p
h
y
s
i
cal
sy
st
em
s have
no
nl
i
n
ea
r c
h
ar
acteristics; hence, linear cont
rollers
fail to
m
e
e
t
th
e requ
irem
en
ts d
u
e
t
o
system n
o
n
lin
ear
ities. Th
e
v
a
riatio
ns an
d
t
h
e non
linear p
a
ram
e
ters su
ch
as gear bac
k
l
a
sh, l
o
a
d
va
ri
at
i
ons a
nd
ot
he
r param
e
t
e
rs have u
n
p
r
e
d
i
c
t
a
b
l
e effect
s on t
h
e co
nt
r
o
l
l
e
d sy
st
em
s
(e.
g
. r
o
b
o
t
m
a
ni
p
u
l
a
t
o
r
)
di
m
i
ni
sh t
h
e pe
rf
o
r
m
a
nce. There
f
ore
,
t
h
e ro
b
o
t
m
a
ni
pul
at
o
r
m
a
y
be consi
d
er
ed as a
linear m
odel
whe
n
it
works
on sm
all
space, or it
has a
large
gea
r
ratio
betwee
n t
h
e
joints a
n
d thei
r links
.
No
nl
i
n
ea
r m
e
tho
d
s
co
nsi
d
ere
d
as
ge
ne
ral
c
a
se w
h
e
n
c
o
m
p
are
d
t
o
l
i
n
ea
r
m
e
t
hods
beca
use i
t
ca
n
be
a
ppl
i
e
d
success
f
ully on
the
linea
r m
e
thods
, but
linear
m
e
thod
is not s
u
fficient to so
l
v
e a
n
d control
nonlinear
p
r
ob
lem
s
.
Co
mmo
n
m
e
th
o
d
o
l
og
ies are u
s
ed
to
so
lv
e the n
o
n
lin
earities in
co
n
t
ro
l syste
m
s su
ch
as slid
in
g
m
ode cont
rol
,
and
st
at
e fee
d
b
ack c
ont
rol
a
r
e
di
sc
usse
d i
n
[
4
]
.
3. CO
NTR
O
L
TECH
N
IQ
U
E
S
Du
e t
o
un
certain
t
y an
d
instabilit
y effects, unk
nown
o
r
un
pred
ictab
l
e inp
u
t
s th
at m
a
n
i
p
u
l
ate th
e p
l
an
t
out
put t
o
the
incorrect ta
rget
. T
h
ese inputs
are called
di
st
ur
ba
nce
or
n
o
i
s
e, s
o
a
n
al
y
z
i
ng a
n
d
desi
g
n
i
n
g t
h
e
math
e
m
atica
l
m
o
d
e
l o
f
th
e syste
m
in
clu
d
e
s th
e con
t
ro
ller an
d
p
l
an
ts t
o
get th
e d
e
sired
b
e
h
a
v
i
or is requ
ired.
M
a
ny
co
nt
rol
t
echni
que
s ha
v
e
been
p
r
o
p
o
se
d t
o
c
ont
rol
r
o
bot
m
a
ni
pul
at
o
r
ra
ngi
ng i
n
co
m
p
l
e
xi
ty
from
l
i
n
ear
t
o
t
h
e a
dva
nc
ed co
nt
r
o
l
sy
s
t
em
, whi
c
h c
o
m
put
e t
h
e r
o
bot
dy
nam
i
c
and
save i
t
f
r
o
m
dam
a
ge i
n
real
envi
ro
nm
ent
s
. Three
di
ffe
re
nt
cont
rol
sc
h
e
m
e
s nam
e
l
y
PID c
o
nt
rol
l
e
r
,
FLC
,
an
d t
h
e fuzzy
su
per
v
i
s
o
r
y
co
n
t
ro
ller
(FSC) will b
e
im
p
l
e
m
en
ted
throug
h
t
h
is article
.
Th
e
p
e
rform
a
n
ce o
f
th
ese contro
llers
will b
e
b
a
sed
on t
h
e
hi
g
h
p
r
eci
si
on i
n
re
d
u
c
i
ng t
h
e
ove
rs
ho
ot
, m
i
nim
i
zing st
ea
dy
st
at
e erro
r,
dam
p
i
ng u
n
wa
nt
ed
vi
brat
i
o
n
of r
o
bot
m
a
nipul
at
o
r
, an
d h
a
ndl
i
n
g t
h
e u
n
p
r
e
d
i
c
t
a
bl
e d
i
st
urba
nces
. PI
D co
nt
rol
l
e
r i
s
one o
f
t
h
e earl
i
e
st
co
n
t
ro
llers in
th
e ind
u
strial
robo
t m
a
n
i
p
u
l
ato
r
s, so
th
e first atte
m
p
t to
con
t
ro
l th
e
plan
t is u
s
e th
e PID
co
n
t
ro
ller. PID co
n
t
ro
ller is still co
n
s
id
ered
th
e m
o
st wi
d
e
ly u
s
ed
i
n
ind
u
stry [5
] and
[6]. Th
e pop
u
l
arity of
usi
n
g t
h
e
PI
D
or t
h
e PI
D
-
t
y
p
e
s co
nt
rol
l
e
r
s
i
s
t
h
at
t
h
ey
ha
ve a si
m
p
l
e
struct
ure, a
n
d t
h
ey
gi
ve sat
i
s
fa
ct
ory
resul
t
s
w
h
e
n
t
h
e re
qui
rem
e
nt
s are reaso
n
a
b
l
e
and t
h
e p
r
oc
ess param
e
t
e
rs vari
at
i
ons a
r
e
l
i
m
i
t
e
d. In ad
di
t
i
on,
th
e m
a
j
o
r
ity of
ap
p
licatio
ns
ar
e fam
i
liar
with
th
e
PID
co
n
t
r
o
ller b
a
sed
o
n
th
e know
ledg
e
o
f
th
e syste
m
charact
e
r
i
s
t
i
c
s. Several
t
ech
n
i
ques
used
fo
r
t
uni
n
g
PI
D p
a
ram
e
t
e
rs t
h
at
have
been
de
v
e
l
ope
d o
v
er t
h
e past
decade
suc
h
as
Ziegler-Nichols (Z-N
) tuning m
e
thods [7].
One
of t
h
e
drawbac
k
s
for using the
PID c
ont
rol
techniques is t
h
at, they are
not su
ffi
ci
ent
t
o
obt
ai
n t
h
e des
i
red t
r
ac
ki
n
g
c
ont
rol
pe
rf
o
r
m
a
nce beca
use
of t
h
e
n
o
n
lin
earity o
f
th
e
ro
bo
t m
a
n
i
pu
lato
r.
Hence, a l
o
t
o
f
time is requ
ired to
t
u
n
e
th
e PID
p
a
ram
e
ters.
On the
ot
he
r han
d
,
ot
her t
ech
ni
q
u
es
are used t
o
ove
rc
om
e t
h
e
pre
v
i
o
us p
r
o
b
l
e
m
,
such as fuzzy
cont
r
o
l
l
e
r t
h
at
e
m
u
l
ates h
u
m
an
o
p
e
ration
.
FLC is an em
erg
i
ng
tech
n
i
q
u
e
in
con
t
ro
l
syste
m
s. It is consid
ered
as in
tellig
en
t
co
n
t
ro
ller. Man
y
stud
ies show th
at th
e
fu
zzy co
n
t
ro
lle
r (FC) p
e
rform
s
su
perior to
con
v
e
n
tion
a
l contro
ller
al
go
ri
t
h
m
s
wi
l
l
be
di
sc
usse
d i
n
t
h
e
ne
xt
sect
i
o
n
.
Za
de
h [
8
]
di
d t
h
e m
a
i
n
i
d
ea o
f
FLC
an
d
fuzzy
set
t
h
eo
r
y
.
M
a
m
d
ani
an
d hi
s
col
l
e
a
gues
[9]
have
d
o
n
e a
pi
o
n
ee
ri
ng
resear
ch wo
rk
o
n
FLC in
th
e mid
-
’7
0 for
engi
ne st
eam
boi
l
e
r
.
The
be
nefi
t
o
f
FLC
i
s
ob
vi
o
u
s
w
h
e
n
t
h
e c
ont
rol
l
e
d p
r
oc
ess i
s
t
o
o com
p
l
i
cat
ed t
o
be
analyzed
using PID controller or whe
n
th
e
in
fo
rm
atio
n
abo
u
t
the con
t
ro
l
l
ed
system
d
o
e
s no
t ex
ist. FLC is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
I
J
RA
Vo
l. 2
,
N
o
. 2
,
Jun
e
201
3
:
5
6
–
68
58
cl
assi
fi
ed i
n
t
o
t
w
o cat
e
g
o
r
i
e
s:
t
h
e fi
rst
,
i
n
vol
ves t
h
e
f
u
z
z
y
l
ogi
c sy
st
em
based
on a
rul
e
base
d o
n
expe
rt
syste
m
, to
d
e
term
in
e th
e con
t
ro
l action
.
Th
e second
u
s
ed
FL to prov
id
e
on
lin
e adj
u
stm
e
n
t
for th
e
p
a
rameters
o
f
th
e co
nv
en
tio
n
a
l con
t
ro
ller su
ch
as th
e PID co
n
t
ro
l [1
0]. Th
is
m
e
th
o
d
atte
m
p
ts
to
co
m
b
in
e th
e
m
e
r
its o
f
FL with
t
h
ose co
n
t
ro
l techn
i
qu
es to
expan
d
t
h
e cap
a
bilit
y o
f
lin
ear co
n
t
ro
l tech
niq
u
e
t
o
h
a
nd
le th
e
n
o
n
lin
earity in th
e
ph
ysical syste
m
. Fu
zzy
sup
e
rv
is
ory
i
s
use
d
t
o
re
du
ce t
h
e am
ou
nt
o
f
t
u
ni
n
g
t
h
e
PI
D
cont
roller
with a fuzzy system
[11]. It
is co
n
s
i
d
ered
as an
attractiv
e m
e
th
od
to so
l
v
e th
e
n
o
n
lin
ear
co
n
t
ro
l
pr
o
b
l
e
m
s
, one of t
h
e adva
nt
ages o
f
fuzzy
supe
rvi
s
ory
t
h
at
t
h
e cont
r
o
l
param
e
t
e
rs chan
ge
d rapi
dl
y
wi
t
h
respect t
o
the
variation
of t
h
e syste
m
response.
The
fuzzy
sup
e
rv
isor
o
p
erates in
a m
a
n
n
e
r sim
ilar to
th
at of
t
h
e FLC
and a
dds a
hi
g
h
er l
e
vel
of c
ont
rol
t
o
t
h
e exi
s
t
i
n
g
sy
st
em
. Fuzzy supe
rvi
s
ory
i
s
hy
bri
d
bet
w
ee
n t
h
e
PID
co
nt
r
o
l
l
e
r
and
FLC
t
h
at
desi
g
n
e
d
t
o
o
v
erc
o
m
e
t
h
e pro
b
l
e
m
of t
uni
ng
PI
D i
n
n
o
n
l
i
n
ear sy
st
em
s usi
n
g
FLC as an ada
p
tive controller [12]. The ba
s
i
c structure
o
f
FSC resem
b
les the structure
o
f
PI
D cont
rolle
r, b
u
t
t
h
e co
nt
r
o
l
l
e
d
param
e
t
e
r of
P
I
D
co
nt
r
o
l
l
e
r
d
e
pen
d
s
o
n
t
h
e
out
put
o
f
t
h
e
f
u
zzy
co
nt
r
o
l
l
e
r
.
4. KINE
M
A
T
I
CS A
N
D
M
A
THEMATI
C
AL MO
DELING
Th
ere are two
main
classes in a ro
bo
t m
a
n
i
pu
lato
r: serial man
i
pu
lato
rs d
e
sig
n
e
d
u
s
ing
an op
en loo
p
ki
nem
a
t
i
c
chai
n a
n
d
pa
ral
l
e
l
m
a
ni
pul
at
o
r
de
si
gne
d
usi
n
g cl
ose
d
l
o
o
p
ki
ne
m
a
t
i
c
chai
ns.
Thi
s
art
i
c
l
e
ha
ndl
es se
ri
al
m
a
ni
p
u
l
a
t
o
rs
. R
o
b
o
t
m
a
ni
pul
at
or c
o
nsi
s
t
s
o
f
a col
l
ect
i
on
of
n-l
i
n
ks t
h
at
co
nn
ected tog
e
th
er
b
y
j
o
i
n
ts.
Each
on
e
o
f
these jo
in
ts h
a
s
a m
o
to
r allo
wi
n
g
th
e m
o
tio
n
to
th
e co
mm
a
n
d
e
d
link. T
h
e m
o
tors
ha
ve fee
d
back sensors to
m
easure
the
out
put (e
.g. position, vel
o
city, and torque) a
t
each
i
n
st
ant
.
Li
n
k
s
and
j
o
i
n
t
s
f
o
r
m
a ki
nem
a
t
i
c
chai
n c
o
n
n
ect
e
d
t
o
gr
ou
n
d
f
r
o
m
one si
de, a
nd t
h
e ot
her i
s
free.
At
t
h
e end
of t
h
e
ope
n si
de
, t
h
e end
-
ef
fect
o
r
s (
e
.g.
gri
ppe
r, w
e
l
d
i
ng t
o
ol
, o
r
anot
her t
o
ol
) a
r
e use
d
t
o
d
o
som
e
tasks as
wel
d
ing,
or ha
ndle
materi
als [2].
Robot m
a
nipul
ator is
nam
e
d
according t
o
num
b
er
of
DOF, which
r
e
f
e
r
s
to th
e nu
m
b
er
of
jo
in
t
s
. As an
ex
amp
l
e,
r
obo
t m
a
n
i
p
u
l
ator
h
a
s
5
j
o
i
n
ts,
wh
ich
mean
th
e
r
obot h
a
s
5
D
OF, an
d so
o
n
.
In
p
h
y
sical app
licatio
n
s
, i
t
is im
p
o
r
tan
t
t
o
d
e
scrib
e
t
h
e
p
o
s
ition
of th
e end
effect
o
r
s
o
f
the
ro
b
o
t
m
a
ni
pul
at
or i
n
o
n
e
gl
o
b
al
c
o
o
r
di
nat
e
s. I
n
t
r
a
n
sf
orm
i
ng,
t
h
e
co
o
r
di
nat
e
s
of
t
h
e
en
d e
ffect
ors
f
r
o
m
t
h
e
lo
cal p
o
s
ition
to
th
e g
l
ob
al positio
n
,
th
e ro
bot
m
o
v
e
m
e
n
t
s a
r
e represen
ted
b
y
a series o
f
m
o
v
e
m
e
n
t
s o
f
rig
i
d
lin
k
s
.
Each
li
nk
d
e
fin
e
s a
p
r
op
er t
r
an
sfo
r
m
a
tio
n
m
a
trix
relatin
g
th
e po
sitio
n of th
e curren
t
lin
k
t
o
th
e prev
i
o
us
one
. As m
e
nt
ione
d p
r
evi
o
usl
y
, rob
o
t
m
a
nipul
at
o
r
w
h
o
s
e
al
l
joi
n
t
s
are pri
s
m
a
t
i
c
i
s
kno
w
n
as a C
a
rt
esi
a
n
man
i
p
u
l
ator wh
ile
th
e robo
t who
s
e
jo
in
t v
a
riab
les
are re
vo
lu
te
is
called an
articu
l
ated
man
i
p
u
l
ator. Fig
u
re 1
sho
w
s a C
a
rt
esi
a
n m
a
ni
pul
at
or wi
t
h
3 ri
gi
d b
o
d
i
e
s an
d t
h
ree
joi
n
t
vari
a
b
l
e
s rep
r
esent
s
t
h
e C
a
rt
esi
a
n
coo
r
di
nat
e
s of
t
h
e
en
d
e
ffe
ct
o
r
ss wi
t
h
re
sp
ect to
th
e
bo
d
y
0
,
wh
ich
is fix
e
d.
Fi
gu
re 1.
R
o
bo
t
m
a
ni
pul
at
o
r
wi
t
h
P
PP j
o
i
n
t
s
B
ody
2 i
s
fi
xe
d t
o
bo
dy
1 a
nd
b
ody
3 i
s
f
i
xed t
o
b
ody
2
.
The e
nd e
ffe
ct
ors
,
b
ody
3 and
i
t
s
m
o
v
e
m
e
n
t
relativ
e to
2
.
Th
e co
ord
i
n
a
te
o
f
t
h
e wrist po
in
t
with
resp
ect t
o
th
e fi
x
e
d bod
y
is:
′
′
(1)
Whe
r
e,
d
1
,
d
2
, and
d
3
are t
h
e
gi
ve
n
ran
g
e
o
f
m
o
ti
on.
Ki
ne
m
a
t
i
c
s i
s
t
h
e m
o
t
i
o
n
geom
et
ry
o
f
t
h
e
ro
b
o
t
man
i
p
u
l
ator fro
m
th
e reference p
o
s
ition
to
th
e d
e
sired
p
o
s
i
tio
n
with
n
o
reg
a
rd
to
fo
rces o
r
o
t
h
e
r
factors th
at
i
n
fl
ue
nce r
o
b
o
t
m
o
t
i
on [3]
.
I
n
ot
her w
o
rds
,
t
h
e ki
nem
a
t
i
c
s
deal
s wi
t
h
t
h
e
m
ovem
e
nt
of t
h
e r
o
b
o
t
m
a
ni
pul
at
or
wi
t
h
respect
t
o
fi
xe
d
fram
e
as a f
u
nct
i
o
n
of
t
i
m
e
. The
fi
xe
d
fram
e
i
n
r
o
b
o
t
re
pre
s
ent
s
t
h
e
base a
n
d al
l
ot
h
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Mo
del
i
n
g
a
n
d
C
ont
r
o
l
of
5
D
OF R
o
bot
Arm
Usi
n
g
Fu
zzy L
ogi
c
S
upe
rvi
s
o
r
y…
(Mo
ham
ma
d Am
in
Ra
sh
i
d
ifa
r)
59
m
ovem
e
nt
s
m
easure
d
fr
om
the b
a
se as
ref
e
rence
.
It
i
s
on
e of th
e m
o
st
fund
am
en
tal
d
i
scip
lin
es i
n
robo
ts,
pr
o
v
i
d
i
n
g t
o
ol
s fo
r d
e
scri
bi
ng t
h
e st
r
u
ct
u
r
e an
d
beha
vi
or
of
r
o
b
o
t
m
a
ni
pul
at
o
r
m
echani
s
m
s
,
and i
t
i
s
im
port
a
nt
i
n
pr
act
i
cal
appl
i
cat
i
ons
suc
h
as
t
r
aject
o
r
y
pl
a
nni
ng
an
d c
o
nt
rol
pu
r
poses
.
Gen
e
ral
l
y
, t
o
c
ont
r
o
l
an
y
ro
b
o
t
m
a
ni
pul
at
or t
h
e c
o
re
o
f
t
h
e
c
ont
r
o
l
l
e
r i
s
a
d
e
scri
p
tio
n of
k
i
n
e
m
a
t
i
c
an
alysis, t
h
is is don
e
b
y
u
s
in
g a
com
m
on
m
e
t
hod
i
n
i
n
d
u
st
ri
al
an
d aca
dem
i
c
researc
h
,
nam
e
l
y
Dena
vi
t
-
Ha
r
t
enbe
rg
m
e
t
hod
[1]
,
[
2
]
an
d
[
3
]
.
The di
st
i
n
ct
o
f
t
h
i
s
m
e
t
hod g
i
ves a m
a
t
h
em
at
i
cal
descri
pt
i
on
fo
r al
l
seri
al
m
a
ni
pul
at
ors
depe
n
d
i
n
g
on t
h
e r
o
b
o
t
g
e
om
et
ry
, and i
t
defi
ne
s t
h
e p
o
s
i
t
i
on an
d o
r
i
e
nt
at
i
on
of t
h
e
cur
r
ent
l
i
n
k wi
t
h
res
p
ect
t
o
p
r
evi
o
us
o
n
e
. In
ad
d
ition
,
it allo
ws t
h
e d
e
sired
frame to
create a set o
f
steps to
b
r
i
n
g
t
h
e o
t
h
e
r lin
k
s
co
ord
i
n
a
te in
to
cor
r
es
po
n
d
i
n
g wi
t
h
an
ot
he
r o
n
e. F
o
r m
o
re i
n
f
o
rm
at
i
on,
re
aders m
a
y
return to the
pre
v
i
ous
refe
rence
s
.
The
k
i
n
e
m
a
tic so
lu
tio
n
in th
is chap
ter
will focus on
two
im
p
o
rtan
t
p
r
o
b
l
em
arises in ro
bo
t
m
a
n
i
p
u
l
ato
r
.
Sectio
n
(2
.2
) di
sc
usses
m
e
t
hod
ol
o
g
i
e
s t
o
sol
v
e t
h
e
fo
rwa
r
d an
d i
n
verse
ki
nem
a
t
i
c respect
i
v
el
y
.
The fi
rst
p
r
o
b
l
em
i
s
d
e
term
in
in
g
the forward
k
i
n
e
matic (FK) where th
e rob
o
t
man
i
p
u
l
ator end
-
effect
o
r
s
will b
e
if all j
o
i
n
t
s
are
known. This
means what ri
gid m
o
ti
on each joint effect on its link to
obt
ain the
desi
red c
o
nfigurati
o
n. The
configuration space of
the
e
n
d-effectors c
ontains the
tra
n
sform
a
tion
matrix T that
re
la
tes the position and
ori
e
nt
at
i
on
o
f
t
h
e e
n
d
-
ef
fect
o
r
s. T
h
e
fol
l
o
wi
n
g
e
quat
i
o
n e
x
p
l
ai
ns t
h
e
fo
r
w
a
r
d
ki
nem
a
ti
c pr
obl
em
.
,
,…,
,
,
,
(2)
Whe
r
e
θ
,
θ
and
θ
are th
e inpu
t
v
a
riab
les,
x
,y
,z
are th
e
d
e
sired
po
sitio
n and
R
th
e
d
e
s
i
r
e
d
rotation. T
h
e s
econd
problem is de
term
ining the inve
rse kinem
a
tic (IK),
whic
h calculat
e
s the val
u
e of each
j
o
i
n
t
v
a
riab
le if th
e d
e
sired
po
sitio
n and
orien
t
atio
n of
end-effecto
r
s are
k
nown. Th
at
mean
s if t
h
e
fin
a
l link
con
f
i
g
urat
i
o
n i
s
kn
o
w
n
,
w
h
at
i
s
t
h
e possi
bl
e con
f
i
g
urat
i
o
n
(e.
g
. sol
u
t
i
o
ns)
of t
h
e r
o
b
o
t
m
a
ni
pul
at
o
r
t
o
m
ove
the end-e
ffect
ors
of t
h
e robot arm
to desired
position a
nd
orie
ntation
in space.
Inve
rse kinem
a
tic p
r
oblem
may expres
s mathem
atically as follows:
,
,
,
,
,…,
(3)
For se
ri
al
m
a
ni
pul
at
o
r
s wi
t
h
r
e
vol
ut
e or
pri
s
m
a
t
i
c
joi
n
t
s
t
h
e FK i
s
deri
ve
d usi
ng
pr
oced
ures s
u
c
h
as
t
h
e DH c
o
n
v
e
n
t
i
on m
a
t
r
i
x
[3]
,
but
i
n
t
h
e pa
ra
l
l
e
l
m
a
ni
pul
at
o
r
, t
h
e f
o
r
w
ar
d
ki
nem
a
t
i
c
be not
easy
t
o
be sol
v
e
d
d
u
e
to
t
h
e co
mp
lex
ity of th
e ro
bo
t m
a
n
i
p
u
l
at
o
r
.
There
f
ore, i
t
m
a
y
sol
v
ed
by
u
s
i
ng a set
o
f
n
o
n
l
i
n
ear e
q
uat
i
o
ns.
On t
h
e ot
h
e
r ha
nd
, sol
v
i
n
g
t
h
e IK
fo
r
p
a
rallel m
a
n
i
p
u
l
ato
r
is easier th
an
FK so
lu
ti
o
n
, and
t
h
ere are m
a
n
y
so
lu
tio
n
s
to
ach
i
ev
e
th
e d
e
si
red
task
. Th
e
secon
d
issu
e t
h
at will
b
e
d
i
scu
ssed
is t
h
e
DC m
o
to
r m
o
d
e
lin
g.
DC m
o
tor m
o
d
e
lin
g is an im
p
o
r
tan
t
issue
b
e
fo
re d
e
sign
in
g a co
n
t
ro
ller
to
kno
w th
e
syste
m
ch
aracteri
s
tics an
d its m
a
th
em
a
tical
m
o
d
e
l.
5
.
DC MOTOR MODELING
Gene
ral
l
y
,
m
odel
i
ng
refe
rs t
o
sy
st
em
descri
pt
i
o
n
in m
a
them
atical ter
m
s, whic
h cha
r
a
c
terizes the
i
n
p
u
t
-
out
put
r
e
l
a
t
i
onshi
p.
Di
rect
cu
rre
nt
(
D
C
)
m
o
t
o
r i
s
a com
m
on a
c
t
u
at
or
f
o
u
n
d
i
n
m
a
ny
m
e
chani
cal
syste
m
s and industrial app
licatio
n
s
su
ch
as in
d
u
strial an
d
edu
catio
n
a
l
robo
ts [3
]. DC
m
o
to
r co
nverts th
e
electrical energy to m
echanical ener
gy
. Th
e
m
o
t
o
r di
rect
l
y
has a rot
a
ry
m
o
t
i
on, a
nd
whe
n
c
o
m
b
i
n
ed wi
t
h
m
echani
cal
pa
r
t
i
t
can
pr
ovi
de
t
r
ansl
at
i
o
n m
o
t
i
on
fo
r t
h
e
des
i
red l
i
n
k.
E
qua
t
i
on
(4
) st
at
es t
h
e
rel
a
t
i
on
bet
w
een
t
h
e cu
rre
nt
a
n
d
de
vel
o
ped
t
o
r
que
i
n
:
(4)
Whe
r
e
τ
t
, is t
h
e m
o
to
r t
o
rq
ue pro
d
u
c
ed
b
y
th
e m
o
to
r
shaft,
φ
th
e m
a
g
n
e
tic fl
u
x
,
i
t
, t
h
e
arm
a
ture curre
n
t, a
nd
K
, is a p
r
op
ortion
a
l
co
nstan
t
. Equatio
n
(5) illu
strates th
e relatio
n
b
e
tween
th
e
p
r
od
u
c
ed
EM
F and
th
e sh
aft
velo
city:
(5)
Whe
r
e
v
, d
e
no
tes th
e
b
a
ck
EM
F, an
d
ω
, is th
e
sh
aft
v
e
lo
city
o
f
th
e m
o
to
r.
DC
m
o
to
rs are i
m
p
o
r
tan
t
in
con
t
ro
l syste
m
s, so
it is
n
ecessary to
estab
lish
and
an
alyze th
e
math
e
m
atica
l
m
o
d
e
l o
f
th
e DC m
o
to
rs. Fig
u
re 2
sh
ows t
h
e sch
e
m
a
tic o
f
th
e arm
a
tu
re co
n
t
ro
lled
DC m
o
to
r
wi
t
h
a fi
xe
d fi
e
l
d
ci
rc
ui
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
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56
I
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Vo
l. 2
,
N
o
. 2
,
Jun
e
201
3
:
5
6
–
68
60
Fi
gu
re
2.
Sc
he
m
a
t
i
c
of DC
m
o
t
o
r sy
st
em
.
It is m
o
d
e
led
as circu
it
with
resistan
ce and
i
n
ductance
connected i
n
series. Th
e inpu
t vo
ltag
e
,
is th
e vo
ltag
e
su
pp
lied b
y
amp
lifier t
o
m
o
v
e
th
e m
o
to
r. The b
a
ck EMF
vo
ltag
e
, is i
n
duced
b
y
t
h
e ro
tatio
n
of t
h
e a
r
m
a
t
u
re wi
n
d
i
n
gs i
n
t
h
e fi
xed
m
a
gnet
i
c
fi
el
d.
To
deri
ve t
h
e t
r
a
n
sfe
r
fu
nct
i
o
n
of t
h
e
DC
m
o
t
o
r
,
t
h
e
sy
st
em
i
s
di
vi
ded i
n
t
o
t
h
ree
m
a
jor com
p
o
n
ent
s
of eq
uat
i
on:
el
ect
ri
cal
equat
i
o
n,
m
echanical equation, and
electro-m
echanical equation
[2
8]
. T
h
e t
r
a
n
s
f
er
f
unct
i
o
n
of
t
h
e m
o
t
o
r s
p
ee
d i
s
:
(6)
In add
itio
n, the tran
sfer fun
c
tio
n
o
f
th
e m
o
to
r
po
sitio
n
is d
e
term
in
ed
by
m
u
ltip
lyin
g
th
e tran
sfer
fun
c
tion
o
f
t
h
e
m
o
to
r sp
eed
by th
e term
:
(7)
Whe
r
e,
, and
,
are
de
not
e
d
as
t
h
e m
o
m
e
nt
of
i
n
ertia an
d m
o
to
r
friction
co
efficien
t.
Acco
r
d
i
n
g t
o
t
h
e
pre
v
i
o
us
di
scussi
o
n
,
t
h
e
s
c
hem
a
t
i
c
di
agram
i
n
Fi
g
u
re
2 i
s
m
odel
e
d
as a
bl
oc
k
d
i
agram
in
Figu
re
3
.
Th
is b
l
ock
d
i
agram
rep
r
esen
ts
an
op
en
loop
system
, an
d th
e m
o
to
r
h
a
s
b
u
ilt-in feed
b
a
ck
EMF,
wh
ich
ten
d
s
to red
u
c
e th
e cu
rren
t
flow.
Fi
gu
re
3.
B
l
oc
k
di
ag
ram
for
DC
m
o
t
o
r sy
st
em
.
Fi
gu
re
4.
DC
m
o
t
o
r su
bsy
s
t
e
m
usi
ng S
I
M
U
LIN
K
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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SN
:
208
9-4
8
5
6
Mo
del
i
n
g
a
n
d
C
ont
r
o
l
of
5
D
OF R
o
bot
Arm
Usi
n
g
Fu
zzy L
ogi
c
S
upe
rvi
s
o
r
y…
(Mo
ham
ma
d Am
in
Ra
sh
i
d
ifa
r)
61
The ad
va
nt
age
of usi
ng t
h
e
bl
oc
k di
ag
ram
gi
ves a cl
ear pi
ct
ure o
f
t
h
e
t
r
ansfe
r
fu
nct
i
on rel
a
t
i
o
n
betwee
n each
bloc
k of the s
y
ste
m
. Therefore, base
d on
the block
diagra
m in Figure
3, the transfe
r
function
fr
om
to
with
0
was illu
strated
in
Eq
u
a
tion
(7
).
Transfer fun
c
tio
n fro
m
th
e lo
ad
torq
u
e
,
to
i
s
gi
ve
n
wi
t
h
0
.
⁄
(8)
Wh
ere, gr, is th
e
g
ear ratio.
Usin
g
SIMULINK, th
e m
o
d
e
l of th
e m
o
to
r
may b
e
created. Th
is m
o
d
e
l inclu
d
e
s
al
l
t
h
e pa
ram
e
ters
deri
ved
p
r
e
v
i
o
usl
y
. Fi
gu
re
4 s
h
ow
s t
h
e
SI
M
U
LI
NK
m
odel
of
DC
m
o
t
o
r
.
To
obtain the
s
t
ate-space
repres
entation of
DC m
o
tor in the
sp
ace m
a
trix, s
t
ate space m
o
del takes
th
e fo
rm
:
(9)
To s
o
lve
DC
motor tra
n
sfe
r
function using
st
ate space:
first, assign the
va
ri
ables.
Let
,
and
. Se
c
o
n
d
,
t
a
ke
t
h
e
f
i
rst
de
ri
vat
i
v
e
of
t
h
e
pre
v
i
o
u
s
sy
st
em
equat
i
o
ns
as
,
and
.
The
state-s
p
ac
e re
presentation
of
DC
m
o
tor in s
p
ace
matrix could
be
expres
sed in
this form
:
0
00
1
0
0
0
(10)
Th
e
ou
tpu
t
equatio
n
is:
010
(11)
Wh
ere A is the syste
m
d
y
n
a
mic
matrix
is
th
e in
pu
t
m
a
tr
ix
, Y is th
e
ou
tpu
t
m
a
trix
an
d
B, C an
d
D are
coefficient m
a
trices.
Tabl
e
1 s
h
o
w
s
DC
m
o
t
o
r
para
m
e
t
e
rs and
val
u
es c
h
osen
f
o
r
m
o
t
o
r sim
u
l
a
t
i
on
.
Tabl
e 1. DC
m
o
t
o
r param
e
t
e
r
and
val
u
es
Para
m
e
ter Value
Mo
m
e
nt of inertia
0
.000052
.
Friction coef
f
i
cient
0
.01
.
Back E
M
F constant
0
.235
T
o
r
que constant
0
.235
Electri
c resistance
2
o
h
m
E
l
ectr
i
c inductance
0
.23
Gear ratio
L
o
ad tor
que
Angular
speed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
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56
I
J
RA
Vo
l. 2
,
N
o
. 2
,
Jun
e
201
3
:
5
6
–
68
62
To study the behavi
or
of the
DC
m
o
tor, c
o
nsider the system
without
dist
urba
nce, the
n
; substitute the
p
a
ram
e
ter v
a
lues of
DC m
o
to
r fro
m
Tab
l
e
1 in
to
Equ
a
tio
n
(7). Th
e
op
en
lo
op
tran
sfer fun
c
tio
n of t
h
e
m
o
to
r
is:
(12)
Equ
a
tio
n
(1
2) can
b
e
written
in
th
e
zero
/po
l
e/g
a
in
form
as:
.
.
(13)
R
e
spo
n
se
o
f
E
quat
i
o
n
(1
3
)
i
s
sh
ow
n i
n
Fi
g
u
re
5.
As
sh
o
w
n;
t
h
e sy
st
em
d
o
es
not
go
t
o
st
eady
st
at
e
v
a
lu
e bu
t to
an in
creasing
v
a
l
u
e. Th
is
m
eans the ar
m
a
ture rotates at a cons
t
a
nt
speed,
whi
c
h i
s
achi
e
ved
by
i
t
s
b
u
ilt-in v
e
l
o
city feedb
a
ck
facto
r
.
Sim
u
l
a
t
i
on res
u
l
t
s
usi
ng
SIM
U
LI
N
K
are
sh
ow
n i
n
Fi
g
u
re
5 an
d
Fi
g
u
re
6
fo
r
DC
m
o
t
o
r
m
odel
wi
t
h
and
wi
t
h
o
u
t
l
o
ad
di
st
ur
ba
nce.
Fig
u
r
e
5
.
D
C
m
o
to
r
op
en loop
step
r
e
spon
se w
itho
u
t
l
o
ad
Fi
gu
re
6.
DC
m
o
t
o
r m
odel
si
m
u
l
a
t
i
on wi
t
h
l
o
ad
di
st
ur
banc
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Mo
del
i
n
g
a
n
d
C
ont
r
o
l
of
5
D
OF R
o
bot
Arm
Usi
n
g
Fu
zzy L
ogi
c
S
upe
rvi
s
o
r
y…
(Mo
ham
ma
d Am
in
Ra
sh
i
d
ifa
r)
63
Si
m
u
latio
n
resu
lts d
e
m
o
n
s
trated
th
at, t
h
e mo
tor run
n
i
n
g
at n
o
-lo
a
d
co
nditio
n
s
at startup
,
and
still
running to reac
h the
steady
state value
as s
h
own i
n
Fi
gure
5.
When a m
echanical l
o
ad is
applied s
u
dde
n
ly to
t
h
e shaft
as sh
ow
n i
n
Fi
g
u
re
6, a sm
al
l
no-l
o
ad c
u
r
r
ent
di
d
not
pr
o
duce e
n
o
u
gh t
o
rq
ue t
o
carry
t
h
e l
o
a
d
;
t
hus
,
th
e m
o
to
r starts to
slo
w
down. Th
is cau
s
e co
un
ters
E
M
F t
o
di
m
i
ni
sh res
u
l
t
i
ng i
n
a hi
g
h
er c
u
r
r
e
n
t
an
d a
cor
r
es
po
n
d
i
n
g
hi
g
h
er t
o
r
q
ue.
Whe
n
t
h
e t
o
r
q
ue de
vel
ope
d
b
y
t
h
e m
o
t
o
r i
s
exact
l
y
equal
t
o
t
h
e t
o
r
que
i
m
pos
ed
b
y
th
e m
ech
an
i
cal lo
ad
, th
en
t
h
e sp
eed
will re
m
a
in
co
nstan
t
.
6
.
FUZ
Z
Y
LOGIC CONT
ROLLER
ST
RUCT
URE
Fi
gu
re 7 sh
o
w
s t
h
e basi
c con
f
i
g
urat
i
o
n o
f
M
I
SO f
u
zzy
sy
st
em
, whi
c
h com
p
ri
ses fo
ur
m
a
i
n
bui
l
d
i
n
g
com
pone
nt
s:
fuzzi
fi
cat
i
on m
e
t
h
o
d
, r
u
l
e
bas
e
, i
n
fere
nce m
echani
s
m
,
and
defuzzi
fi
cat
i
on m
e
t
hod
. As seen i
n
t
h
e fi
gu
re, t
h
e i
n
p
u
t
a
n
d
o
u
t
p
u
t
dat
a
o
f
FLC
a
r
e cri
s
p
(n
o
n
-
f
u
zzy
)
val
u
es
. F
L
C
com
pone
nt
s are:
1. The fuzzifie
r
:
m
easure the values
of in
pu
t
v
a
riab
le and
co
nv
ert th
e in
p
u
t crisp
v
a
lu
es in
to
su
itab
l
e
l
i
ngui
st
i
c
vari
a
b
l
e
s.
2
.
An
exp
e
rt an
d
sk
illed
o
p
e
rato
r d
e
fin
e
th
e
k
nowledg
e b
a
se. Th
e ru
le-b
ase h
o
l
d
s
th
e
k
n
o
w
led
g
e
, in
t
h
e f
o
rm
of
a s
e
t
of
r
u
l
e
s,
of
h
o
w
best
t
o
c
o
nt
rol
t
h
e sy
st
em
.
3. T
h
e i
n
fe
rence m
echanis
m
evaluates
whic
h control
ru
les
are relev
a
n
t
for th
e cu
rren
t time an
d
then
deci
des
w
h
at
t
h
e i
n
p
u
t
t
o
t
h
e
pl
ant
s
h
oul
d
be
.
4. T
h
e
defuzzi
fier is the
opposite
operat
or of fuz
z
ifier
int
e
rface;
it converts the c
oncl
u
sions
reac
he
d
by an infere
nc
e m
echanis
m
into a
real
v
a
lu
e as inpu
ts to
p
l
an
t.
Fi
gu
re
7.
F
u
zz
y
cont
rol
sy
st
e
m
st
ruct
ure
Before illustrating F
L
C com
pone
nts, it is im
portant
to
defi
ne the F
L
C inputs a
n
d output variables
.
The c
ont
roller
is used to c
o
rrect the error signal t
h
en
sup
p
ly ap
p
r
op
riate
in
pu
t to
th
e
p
l
an
t. Two
i
n
pu
t
s
are
use
d
fo
r FLC
:
t
h
e err
o
r t
h
at
g
e
nerat
e
d fr
om
t
h
e feed
bac
k
l
o
o
p
an
d
deri
va
t
i
v
e of t
h
e er
r
o
r, o
r
i
t
m
a
y
al
so ha
ve
an
in
tegral in
pu
t for fu
zzy lik
e PI con
t
ro
ller. In
add
itio
n, wh
en
d
e
sign
ing
a fu
zzy lik
e PID con
t
ro
ller the th
ree
in
pu
ts are used, and
t
h
e
o
u
t
p
u
t is a con
t
ro
l si
g
n
a
l
feed
s th
e
p
l
an
t.
The t
h
ree
varia
b
les
e
,
∆e
a
n
d
u
of
the FLC
are
the error, erro
r
c
h
an
ge,
a
n
d
t
h
e
out
put
act
i
o
n
,
and
t
h
e
vari
a
b
l
e
s
̃
,∆
̃
,
are
th
eir
fu
zzy cou
n
t
erp
a
rts
respectiv
ely, y is th
e
ou
tpu
t
, an
d r is th
e set
po
in
t,
is t
h
e
scale factor
of
the error i
n
put,
k is the
scale
factor of
t
h
e
e
r
ror deri
vative, and
the
i
s
t
h
e
out
put
gai
n
.
Figu
re 8 s
h
o
w
s the effect of
fuzzy
PD a
nd
fuzzy
PI c
ontr
o
ller. Ass
u
m
e
the refe
rence i
n
p
u
t r = 60
im
ple
m
ented for t
h
e
DC m
o
tor. T
h
e res
p
onse sh
ows that
the fuzzy PD
has a
faster
re
sponse
0
.
2
than fuzzy PI
0
.
3
. Th
is m
ean
s th
at th
e fu
zzy
PD con
t
ro
ller
risin
g
tim
e is l
e
ss 33
% th
an
fu
zzy
PI
rising
tim
e
. H
o
we
ve
r, t
h
e f
u
zzy
PD c
o
ntr
o
ller has la
rge
steady
sate er
r
o
r
SSE
0.04
tha
n
t
h
e fuzzy PI
cont
roller w
h
er
e
SSE
0.002
.
Fi
gu
re
8.
O
u
t
p
ut
o
f
fu
zzy PD and
fuzzy
PI for
r
= 60
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
I
J
RA
Vo
l. 2
,
N
o
. 2
,
Jun
e
201
3
:
5
6
–
68
64
7
.
RESULT
Th
e
p
r
opo
sed
co
n
t
ro
llers will b
e
u
s
ed
t
o
con
t
ro
l th
e
Lynx
6
robo
t arm
as a case stud
y.
Lyn
x
6
is an
articulated m
a
nipulator RRR,
with 5DOF,
5 rotational joi
n
ts. T
h
e
robo
t m
ounted with m
oving gri
ppe
r
at
the
en
d of
t
h
e ch
ain
.
Figu
r
e
9 show
s the Lynx6
ro
bo
t ar
m
.
Fig
u
r
e
9
.
Lynx6
r
obo
t
ar
m
The
5
joi
n
ts are nam
e
ly as the base, shoulder, elbow
,
wrist, and
gripp
e
r
d
e
sign
ed
to
cat
ch
an
d
ho
ld
work pieces re
spectively.
A dedicated
se
rvom
otor controls
each of these
jo
ints; these m
o
tors a
r
e connec
ted to
a ser
i
al ser
v
o
co
n
t
r
o
ller
car
d
(
SSC
3
2
)
to
co
n
t
r
o
l th
e Ly
nx
6
f
r
o
m
a co
m
p
u
t
er
th
r
ough
th
e ser
i
al por
t. A
s
m
e
nt
i
oned
p
r
e
v
i
o
usl
y
, t
h
i
s
t
h
esi
s
was
di
sc
us
sed t
h
e m
e
t
hod
t
o
m
odel
an
d
cont
rol
s
t
h
e
di
f
f
ere
n
t
ki
nd
s
of
ro
b
o
t
man
i
p
u
l
ator wi
th
ou
t reg
a
rd
ing
to
th
e
nu
m
b
er of jo
in
t
v
a
ri
a
b
l
e
an
d i
t
s
t
y
pes. Ly
n
x6
r
o
b
o
t
arm
was chose
n
as a
case stu
d
y
du
e to
its s
m
a
ll s
i
z
e
, lig
h
t
weigh
t
,
an
d
it is in
ex
p
e
n
s
iv
e un
lik
e ind
u
s
t
r
ial ro
bo
ts
su
ch
as PUMA 5
6
0
.
In
add
itio
n, if
an
y k
i
n
d
of
rob
o
t
m
a
n
i
p
u
l
at
or availa
b
l
e th
e
m
o
d
e
lin
g
pro
c
ed
ure
will b
e
t
h
e sam
e
. Figu
re 6
.
2
d
e
p
i
cts a g
e
ometric
m
o
d
e
l fo
r th
e Ly
n
x
6
robo
t arm
,
wh
ich
will b
e
u
s
ed
fo
r its k
i
n
e
m
a
tics d
e
riv
a
tion
.
Th
e
joi
n
t
an
gl
es o
f
Ly
nx
6
a
r
e
,
,
,
and
.
Fi
gu
re 1
0
. Fra
m
e
assi
gnm
ent
fo
r
th
e Ly
n
x
6 ro
bo
t ar
m
Tabl
e
2 s
h
o
w
s
t
h
e D
H
pa
ram
e
t
e
rs o
f
Ly
nx
6
r
o
b
o
t
a
r
m
.
Table 2
.
D
H
p
a
ram
e
t
e
r
of
Ly
nx
6 r
o
b
o
t
arm
L
i
nk Joint
1 0-
1
0
90
°
8
2 1-
2
12
0
0
3 2-
3
12
0
0
4 3-
4
6
90
°
0
5 4-
5
0
0
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Mo
del
i
n
g
a
n
d
C
ont
r
o
l
of
5
D
OF R
o
bot
Arm
Usi
n
g
Fu
zzy L
ogi
c
S
upe
rvi
s
o
r
y…
(Mo
ham
ma
d Am
in
Ra
sh
i
d
ifa
r)
65
Fo
r testing
th
e
5
D
OF
Lyn
x
6
robo
t
arm
,
th
e
j
o
i
n
t
d
e
sired in
pu
t ang
l
es are
θ
{
120
°
,6
6
°
,
100
°
,4
5
°
,1
5
°
with
in
itial p
o
s
ition o
f
th
e rob
o
t
arm
is th
e h
o
m
e
p
o
s
ition
θ
0
°
,0
°
,0
°
,0
°
,0
°
. Figure 11
show
s t
h
e ho
m
e
p
o
s
ition fo
r th
e Lynx6
an
d Fi
g
u
r
e
12
sh
ow
s th
e
fin
a
l co
nfigu
r
atio
n
for th
e inpu
t jo
in
t
v
a
riab
l
e
s.
In
o
r
de
r t
o
a
s
s
e
ss t
h
e e
ffi
cac
y
of t
h
e p
r
op
os
ed c
ont
r
o
l
l
e
r,
s
i
m
u
l
a
t
i
on st
u
d
i
e
s ha
ve
been
c
o
n
d
u
ct
ed t
o
check t
h
e effic
i
ency of t
h
e sy
ste
m
. PID c
ont
roller is test
ed
as th
e first attem
p
t
to
con
t
ro
l
th
e Lynx
6
robo
t arm
.
Fig
u
r
e
1
3
, Fi
gu
r
e
14
an
d
Figu
r
e
15
sh
ow
t
h
e
o
u
t
p
u
t
r
e
spo
n
s
e of
th
e mo
tor
s
o
f
t
h
e 5D
OF Lynx6
usin
g
PID
cont
rollers
.
Fig
u
re
11
. Ly
nx
6 ho
m
e
p
o
s
itio
n
Fig
u
re
12
. Ly
nx
6 d
e
sired po
si
tio
n
Figure 13. PID
contro
l step
re
sponse
for
,
Figure 14. PID
contro
l step
re
sponse
for
Evaluation Warning : The document was created with Spire.PDF for Python.